Alden Waters
Published 2013-11-07, updated 2015-10-01Version 2
We prove a logarithmic stability estimate for the time dependent X-ray transform on $\mathbb{R}_t^+\times\mathbb{R}^n$. To do so, we extend a known result by Begmatov for the stability of the time dependent X-ray transform in $\mathbb{R}^+_t\times\mathbb{R}^2$. We give some examples of stability and injectivity results in relationship to the Dirichlet-to-Neumann problem. In particular, under the Geometric Control Condtion, we derive inverse logarithmic stability estimates for time dependent conformal factors.
Comments: this arxiv submission has been split into two separate submissions by separate authors, http://arxiv.org/abs/1406.4854 and the current version. the new version contains a extension to conformal factors
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